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I'll third the kettlebell recommendation.
The old school kettlebell lifts are great for training joint mobility and stability. Not to mention some of the swings are great for developing explosive hip strength which is what you need in any sport to generate lots of power.
As far as conditioning. Nothing beats practice practice practice of the actual sport itself.
I will fourth the kettlebell recommendation. Its great. And also I second Primal's recommendation for conditioning. Nothing beats conditioning for the sport than doing the actual sport. When I wrestled the only way to get in wrestling shape was to wrestle. That is why my coach would have at least one or 2 days a week where the entire 2 hour practice was just straight hard wrestling.
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Of course you should train strength. However, train max strength, NOT hypertrophy. This way you get dense, strong muscles which aren't bloated and huge.
1-5 reps or 1-5 sets. Lower is more strength. 3x3 is good. Work with as heavy as you can manage.
This I must disagree with. Its not about max strength its about strength over time. You don't want to go hard and strong for 3 minutes then be gassed the rest of the fight. Thats why you should train with high reps. In my routine I have at least 2 exercises per muscle group where I perform at least 20 reps, the highest being about 60. In a little bit I'm going to post a routine that is excellent for martial artists, mixed martial artists, wrestlers, and football players because those are all anaerobic sports so stay tuned for that.